4 The table below shows the probability distribution for the number of students, \(R\), attending classes for a particular mathematics module.
| \(\boldsymbol { r }\) | 6 | 7 | 8 |
| \(\mathbf { P } ( \boldsymbol { R } = \boldsymbol { r } )\) | 0.1 | 0.6 | 0.3 |
- Find values for \(\mathrm { E } ( R )\) and \(\operatorname { Var } ( R )\).
- The number of students, \(S\), attending classes for a different mathematics module is such that
$$\mathrm { E } ( S ) = 10.9 , \quad \operatorname { Var } ( S ) = 1.69 \quad \text { and } \quad \rho _ { R S } = \frac { 2 } { 3 }$$
Find values for the mean and variance of:
- \(T = R + S\);
- \(\quad D = S - R\).